Make sure however, that you always get the BIOS executable and NOT the Windows executable.
Most manufacturers provide a Windows executable or a BIOS executable that can only be run under Windows.
Then, after mounting the flash drive, select under distribution Free DOS and your mounted stick.
The app will automatically download the image for you and copy it to the drive.
(Dell offers this as a possibility on their site) Some notes before starting: If your flash image is too large for a floppy, go to the Free Dos bootdisk website, and download the 10Mb hard-disk image.
This image is a full disk image, including partitions, so adding your flash utility will be a little trickier: First find the first partition (at time of writing, the first partition starts at block 63; this means that the partitions starts at offset thus leaving more space for the flash utility and new BIOS image. Copy your BIOS flash utility and new BIOS image to the mounted floppy disk image.